Relationship between the sensor size and focal length
The focal length doesn't change with sensor size. A lens with a 35mm focal length is always 35mm. However, the FOV changes for the same focal length with different sensor size.  

The reason for the common misconception that the focal length gets longer with a smaller sensor, is that lens and camera manufacturers often (if not always) tell us that for instance "This 50mm lens on this camera is equivalent to an 80mm lens on a 35mm sensor". What this means, is that on a Canon APS-C sensor1 a 50mm lens gives the same FOV as an 80mm lens would on a fullframe 35mm2 sensor.  

Crop factor on Wikipedia explains it quite well.  



1Nikon has a different crop factor, so a 50mm lens on one of their cropped sensors would be equivalent to 75mm on a fullframe.
2A fullframe 35mm sensor is actually 36mmx24mm. 35mm comes from the fact that film is 35mm wide, including the edges above and below the recorded image.